麻豆传媒团队

390 Quick Answers 21 April

I will not have office hours during GREAT Day. Make a plan to participate and tell us about it on Friday.

Work on your papers and final topics.

After GREAT Day, we only have chapter 11. We鈥檙e getting there! Remember how busy we were with mathematics in the 19th century in Europe? The 20th century will be like that, not like the slow US chapter. There is _NOT_ less mathematics being done in the 19th century. Definitely not. The US is backwards and trying to catch up, and Jeff and I are struggling to talk about the mathematics because it's sophisticated and we don't know what to do. This is important - there is more mathematics in the 20th century than all of history before. Do NOT miss this big point.

Today we will have a special supplement on the history of linear algebra.

鈥淲hy aren鈥檛 we required to learn ___?鈥� Because there is only so much space for requirements. However, there is and was no limit on what you _choose_ to do. For those who are finishing - it was your choice to not do more. For those not yet finishing - perhaps you will learn from the laments of others. Look for interesting things to study. There are plenty of opportunities.

Someone was surprised at the correlation of dates. As always - keeping a timeline is _so_ important to see how different stories fit together. Don鈥檛 take this lightly. I have good news for you regarding this - chapter 11 is worldwide and chronological. So, get your timelines fixed up now and you鈥檒l be all set.

Statisticians often don鈥檛 think of themselves as mathematicians. Their history is rather separate. Probability is a branch of mathematics, and statistics is on its own, which is why we almost do nothing with statistics. That being said, there are a couple of good GREAT Day projects on statistics (it is always a nice area for 390 projects, since we don鈥檛 touch it in class).

Lecture Reactions

The complex numbers _do_ commute (and it's important that you know that). Only when we go up to the 4-dimensional quaternions, they do not commute.

The point of Thomas Jefferson is that he was _not_ a mathematician, and dismissive of mathematics in general.

If you want to know more about _Alice's Adventures in Wonderland_, please do open and look at the NYT article.

As an aside: Bowditch and Adrain did consider what would mean for a star to be so massive that it captured its own light with its gravity. While this is related to black holes, it鈥檚 not exactly the same and not understood the way it would be 100 years later.

Yes, a good part of 10.1 was not USian. That is because the US is still very thin. There isn't much mathematics in 10.2 either.

Hamilton took a path of invention to devise quaternions. This is the way math is invented. You have properties you want, as he did, and you see what would lead to those properties. He wanted to create a mathematical model of three dimensions, and along the way he surprised himself to realise that to do so he needed four dimensions.

The fact that quaternions were more extensively studied by humans before vectors is fascinating. Why did we decide on vectors? Extend more easily to higher dimensions, no pesky negative sign, and simpler derivation and introduction (as I'm sure you would all agree). Quaternions were a big deal when they were discovered, but they were mostly subsumed by vectors, largely because of leadership like Gibbs and others. This is how they led to many modern ideas (vectors including dot products and cross products, gradient, divergence, curl), but also sound unfamiliar.

Reading Reactions

Remember since we're now at this time in our reading in the US 鈥� 麻豆传媒团队 Normal School was founded in 1871. Again, if you want to know our curriculum, that is what was mostly in my research.

I think of a parallel between the pope doing division and the president proving the multicultural right triangle theorem. Neither would be significant if the person were not significant.

"What is the significance of a journal? What makes them so necessary?" They are a way to disseminate mathematics. Also a way to know that mathematics is reliable - has been checked. We have seen repeatedly that journals are central to building mathematics culture and community. Having a place where work can be shared and read with confidence is the way that a community learns mathematics together. The remains active.

Interesting question when was first ever PhD in the world? One answer that is fun "The first PhD (Doctor of Philosophy) degree was awarded to Al-Kindi (also known as Alkindus) in the 9th century. Al-Kindi was an Arab philosopher, mathematician, and scientist who lived from 801 to 873." That may be a stretch. More reasonable by 1150 in Paris. Definitely by 18th century. .

Somehow this is difficult for me to track down, but Gibbs may be the first PhD in mathematics in the US in 1863. And in 1886 Winifred Edgerton Merrill became the first woman to earn a PhD in mathematics in the US.

Yes, University of Chicago was and is a big deal. It really defined US mathematics.

Good point - yes there are mathematics associations around the world. I don't know much about their history in Europe, but they are there. I can see the reasonable question about why don't we discuss them. . There are national and international meetings. I will talk more about the national ones today - it's one of our main topics.

Having someone go from being the president of Princeton University to the US President is 鈥� stunning, and 鈥� nothing like this has happened again (in this country; it is common in others). The rarity of this may be a strong statement of how education is viewed in this country. If you're interested, compare the education of the new/current Canadian prime minister.

George Hill used infinite determinants and periodic differential equations in his study of the three-body problem in astronomy. His proof showed that the moon is not potentially leaving sometime.

Complex numbers show up in electricity and magnetism because they are the best way to mathematically model two dimensional phenomena. I won鈥檛 be heading in the physics direction during lecture today.

Definitely it remains important to keep up-to-date on what鈥檚 happening in Europe. Everyone is trying to do that as best as is possible. It鈥檚 easier to the end of the 19th century than it was to the beginning. Not as easy as it is today.